Conventionally, an auto-tuning controller such as shown in FIG. 19 has been adopted. This type of controller is recited in an article by A. B. Corripio, P. M. Tompkins, "Industrial Application of a Self-Tuning Feedback Control Algorithm", ISA Transactions, vol. 20, No. 2, 1981, pp 3 to 10. In FIG. 19, the reference numeral 1 designates a reference value signal generator, the reference numeral 502 designates an auto-tuning controller, the reference numeral 3 designates a controlled system, the reference numeral 4 designates a PID (Proportional Integral-Derivative) controller, the reference numeral 5 designates a mathematical model operator, the reference numeral 6 designates an identifier, and the reference numeral 7 designates an adjustment operator.
The operation of this device will now be described.
The auto-tuning controller 502 receives a reference value signal r(k) which is output from the reference value signal generator 1 and a controlled variable y(k) which is output from the controlled system 3, and outputs a manipulated variable u(k) which is to be input to the controlled system 3. The values in parenthesis represent discrete timings at respective sampling intervals.
The operation within the auto-tuning controller is as described below.
First, an error e(k) between the reference value signal r(k) and the controlled variable y(k) is calculated. EQU e(k)=r(k)-y(k) (1)
The PID controller 4 receives the error value e(k), and calculates the manipulated variable u(k) based upon previously established control parameters and outputs the same. The control parameters in the PID controller 4 are the gain K.sub.C, integration time T.sub.I, and differentiation time T.sub.D, and the manipulated variable u(k) is calculated from these parameters according to the following equation. EQU u(k)=u(k-1)+Kc[e(k)-e(k-1)+T/T.sub.I e(k) EQU +T.sub.D /T{e(k)-2e(k-1)+e(k-2)}] (2)
The manipulated variable u(k) is inputted to the controlled system 3 as well as the mathematical model operator 5 and the identifier 6.
The mathematical model operator 5 calculates an output v(k) from the input manipulated variable u(k), for example, according to the following formula. EQU v(k)=a.sub.1 v(k-1)+a.sub.2 v(k-2) EQU +b.sub.1 u(k-m-1)+b.sub.2 u(k-m-2) (3)
Herein, m is an integer larger than or equal to 0, which signifies a dead time.
The identifier 6 determines the coefficients a.sub.1, a.sub.2, b.sub.1, and b.sub.2 of the formula (3) such that the input-output relation of the controlled system 3 and that of the mathematical model operator 5 are equivalent to each other, that is, the outputs y(k) and v(k) of both circuits are equal to each other. For this purpose, the identifier 6 receives the manipulated variable u(k), the controlled variable y(k), and the output of the mathematical model v(k) as its inputs.
For the description of the operation of the identifier 6, the following vectors x(k), z(k), and .phi.(k) are defined. EQU x.sup.T (k-1)=[y(k-1), y(k-2), u(k-m-1), EQU u(k-m-2)] (4) EQU z.sup.T (k-1)=[v(k-1), v(k-2), u(k-m-1), EQU u(k-m-2)] (5) EQU .phi.(k)=[a.sub.1, a.sub.2, b.sub.1, b.sub.2 ] (6)
Herein, the suffix T of the vector represents a transport of the vector.
The identifier 6 executes the next algorithm. EQU G(k)=[1+z.sup.T (k)P(k).times.(k)].sup.-1 z.sup.T (k)P(k) (7) EQU .phi.(k+1)=.phi.(k)+[y(k+1)-.phi.(k).times.(k)]G(k) (8) EQU P(k+1)=P(k)-P(k).times.(k)G(k) (9)
The vector .phi.(k), that is, the coefficients a.sub.1, a.sub.2, b.sub.1, and b.sub.2 of the mathematical model formula (3) are obtained successively by this algorithm.
The vector .phi.(k) which is obtained in this way is output from the identifier 6, sent to the mathematical model operator 5 to be used for modifying the mathematical model formula, and is sent to the adjustment operator 7 to be used for obtaining the control parameters, that is, the gain K.sub.C, integration time T.sub.I, and differentiation time T.sub.D. The adjustment operator 7 conducts the following operation in order to obtain these control parameters. EQU K.sub.C =[a.sub.1 +2a.sub.2 ]Q/b.sub.1 ( 10) ##EQU1##
Herein, Q which appears in the formulae (10) and (12) is defined by the following formula. EQU Q=l-e.sup.-T/B ( 13)
Herein, B is an adjustment parameter, and in more specifically, a desired time constant in a closed loop.
The gain K.sub.C, integration time T.sub.I, and differentiation time T.sub.D obtained in this way are inputted to the PID controller 4 to be again used for calculating the manipulated variable u(k) from the error e(k) using the formula (2).
In this prior art auto-tuning controller with such a construction the identification of the controlled system must be conducted, and there are the following problems in this identification.
(1) The calculation is very complicated.
(2) The quantity of the calculations amounts to a large volume.
(3) It takes a long time for the calculation to converge.
(4) It is impossible to deal with the non-linearity possessed by the controlled system.
(5) This controller is improper for the identification of a controlled system of the type other than that which is determined by the mathematical model formula (3) because the type of mathematical model is restricted to that of the formula (3) in this controller.
(6) There arises redundancy because the four coefficients a.sub.1, a.sub.2, b.sub.1, and b.sub.2 are identified in order to obtain the three control parameters K.sub.C, T.sub.I, and T.sub.D.
These problems in the identification have been problems in the performance of the prior art auto-tuning controller.